Practice Problems Probability
... as any women. (i) Find the probability that a woman wins the tournament. (ii) If m1 and ...
... as any women. (i) Find the probability that a woman wins the tournament. (ii) If m1 and ...
Compactness Theorem for First-Order Logic
... Let G be any set of formulas of first-order logic. Then G is satisfiable if every finite subset of G is satisfiable. ...
... Let G be any set of formulas of first-order logic. Then G is satisfiable if every finite subset of G is satisfiable. ...
+ Section 5.1 Randomness, Probability, and Simulation
... At a local high school, 95 students have permission to park on campus. Each month , the student council holds a “golden ticket parking lottery” at a school assembly. Two lucky winners are given reserved parking spots next to the main entrance. Last month, the winning tickets were drawn by a student ...
... At a local high school, 95 students have permission to park on campus. Each month , the student council holds a “golden ticket parking lottery” at a school assembly. Two lucky winners are given reserved parking spots next to the main entrance. Last month, the winning tickets were drawn by a student ...
this will live in learning village
... Probability: predicts how likely or unlikely something is to occur Probability measures will fall between 0 and 1 as a fraction or a decimal. ...
... Probability: predicts how likely or unlikely something is to occur Probability measures will fall between 0 and 1 as a fraction or a decimal. ...
Discrete/Binomial Notes
... Let x be the number of gallons required to fill a propane tank. Suppose that the mean and standard deviation is 318 gal. and 42 gal., respectively. The company is considering the pricing model of a service charge of $50 plus $1.80 per gallon. Let y be the random variable of the amount billed. What ...
... Let x be the number of gallons required to fill a propane tank. Suppose that the mean and standard deviation is 318 gal. and 42 gal., respectively. The company is considering the pricing model of a service charge of $50 plus $1.80 per gallon. Let y be the random variable of the amount billed. What ...
12.4 Probability of Compound Events
... prize is called, the winning ticket is returned to the drawing box and is eligible to be picked for anther prize. What is the probability that at least one of the tickets is drawn twice? ...
... prize is called, the winning ticket is returned to the drawing box and is eligible to be picked for anther prize. What is the probability that at least one of the tickets is drawn twice? ...
(1997). Sharpness of second moment criteria for branching and tree
... Trees with the same polar sets are denoted equipolar by Pemantle and Peres (1994). In particular, letting {X(v)} be uniform on the unit interval and letting B = {(x1 , x2 , . . .) : ∀n xn ≤ pn }, one sees that equipolar trees Γ1 and Γ2 are percolation equivalent, meaning that: If vertices of both tr ...
... Trees with the same polar sets are denoted equipolar by Pemantle and Peres (1994). In particular, letting {X(v)} be uniform on the unit interval and letting B = {(x1 , x2 , . . .) : ∀n xn ≤ pn }, one sees that equipolar trees Γ1 and Γ2 are percolation equivalent, meaning that: If vertices of both tr ...
Section 4: Random Variables and Probability
... out. The random variable X that describes this experiment would take the values 1 and 2, the outcomes of the experiment, and the associated probabilities would be 12 for each outcome. Note that the specific experiment doesn’t really matter. A gamble where rolling an even number on a fair die pays ou ...
... out. The random variable X that describes this experiment would take the values 1 and 2, the outcomes of the experiment, and the associated probabilities would be 12 for each outcome. Note that the specific experiment doesn’t really matter. A gamble where rolling an even number on a fair die pays ou ...
Students-chapter5-S07
... Unusually high: x successes among n trials is unusually high if P(x or more) is very small (such as less than 0.05) Unusually low: x successes among n trials is unusually low if P( or fewer) is very small (such as less than 0.05) ...
... Unusually high: x successes among n trials is unusually high if P(x or more) is very small (such as less than 0.05) Unusually low: x successes among n trials is unusually low if P( or fewer) is very small (such as less than 0.05) ...
CS 70 Discrete Mathematics and Probability Theory Spring 2016
... up keys, then try them in order, we see that this is equivalent to our earlier scheme. Furthermore, the right key is now equally likely to be in any of the five spots. 2. In an arcade, you play game A 10 times and game B 20 times. Each time you play game A, you win with probability 1/3 (independentl ...
... up keys, then try them in order, we see that this is equivalent to our earlier scheme. Furthermore, the right key is now equally likely to be in any of the five spots. 2. In an arcade, you play game A 10 times and game B 20 times. Each time you play game A, you win with probability 1/3 (independentl ...
Infinite monkey theorem
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.In this context, ""almost surely"" is a mathematical term with a precise meaning, and the ""monkey"" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. One of the earliest instances of the use of the ""monkey metaphor"" is that of French mathematician Émile Borel in 1913, but the first instance may be even earlier. The relevance of the theorem is questionable—the probability of a universe full of monkeys typing a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero). It should also be noted that real monkeys don't produce uniformly random output, which means that an actual monkey hitting keys for an infinite amount of time has no statistical certainty of ever producing any given text.Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. The history of these statements can be traced back to Aristotle's On Generation and Corruption and Cicero's De natura deorum (On the Nature of the Gods), through Blaise Pascal and Jonathan Swift, and finally to modern statements with their iconic simians and typewriters. In the early 20th century, Émile Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics.